论文标题
tableaux的Hopf代数的原始元素
Primitive Elements of the Hopf Algebras of Tableaux
论文作者
论文摘要
对称群体的性格理论以及对称函数的理论都利用了年轻Tableaux的组合，例如Robinson-Schensted算法，Schuetzenberger的“ Jeu de Taquin”和撤离。 1995年，Poirier和第二作者引入了一些代数结构，与多形的质体诱导了一些产物和副作用，这些代数结构不同。 Their starting point are the two dual Hopf algebras of permutations, introduced by the authors in 1995. In 2006 Aguiar and Sottile studied in more detail the Hopf algebra of permutations: among other things, they introduce a new basis, by Moebius inversion in the poset of weak order, that allows them to describe the primitive elements of the Hopf algebra of permutations.在本说明中，通过类似的方法，我们使用TABLEAUX的部分顺序确定了Tableaux的Poirier-Reutenauer代数的原始元素。
The character theory of symmetric groups, and the theory of symmetric functions, both make use of the combinatorics of Young tableaux, such as the Robinson-Schensted algorithm, Schuetzenberger's "jeu de taquin", and evacuation. In 1995 Poirier and the second author introduced some algebraic structures, different from the plactic monoid, which induce some products and coproducts of tableaux, with homomorphisms. Their starting point are the two dual Hopf algebras of permutations, introduced by the authors in 1995. In 2006 Aguiar and Sottile studied in more detail the Hopf algebra of permutations: among other things, they introduce a new basis, by Moebius inversion in the poset of weak order, that allows them to describe the primitive elements of the Hopf algebra of permutations. In the present note, by a similar method, we determine the primitive elements of the Poirier-Reutenauer algebra of tableaux, using a partial order on tableaux defined by Taskin.
